1 Preferred Experiment

1.1 Across prefs

1.2 Movement Duration

Table 1.1: Movement duration linear models.
Duration Linear Estimate P-Value Std Error
Circle 3.398e-02 0.000e+00 1.018e-03
Pilot 4.066e-02 0.000e+00 5.330e-04
Arc 3.665e-02 0.000e+00 9.492e-04
All 3.764e-02 0.000e+00 4.590e-04
Table 1.1: Movement duration average values (s)
Effective Mass (kg) 2a 2b 2c
2.5 0.764±0.038 0.823±0.031 0.632±0.036
3.8 0.83±0.041 0.881±0.033 0.703±0.034
4.7 0.856±0.042 0.905±0.034 0.741±0.043
6.1 0.89±0.043 0.959±0.036 0.781±0.048

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur ~ factor(targetnum) + eff_mass * factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.7201709  0.0296551  24.285  < 2e-16 ***
## factor(targetnum)2 == 0         -0.0653049  0.0017152 -38.075  < 2e-16 ***
## factor(targetnum)3 == 0         -0.0067108  0.0017313  -3.876 0.000106 ***
## factor(targetnum)4 == 0         -0.0394681  0.0017155 -23.007  < 2e-16 ***
## eff_mass == 0                    0.0339780  0.0008742  38.866  < 2e-16 ***
## factor(exp)pilot == 0           -0.1469007  0.0382529  -3.840 0.000123 ***
## factor(exp)smallt == 0           0.0442074  0.0418978   1.055 0.291369    
## eff_mass:factor(exp)pilot == 0   0.0067011  0.0011208   5.979 2.25e-09 ***
## eff_mass:factor(exp)smallt == 0  0.0026912  0.0012137   2.217 0.026598 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on movement duration (slope = 3.398e-02, p = 0.000e+00).

Experiment 2b movement duration is not different from 2a (p = 2.914e-01).

Experiment 2c movement duration is significantly lower than 2a (slope = -1.469e-01, p = 1.229e-04).

The interesting thing with these are the interaction effects.

Experiment 2b movement duration increases with mass more than experiment 2a (slope = 2.691e-03, p = 2.660e-02).

Experiment 2c movement duration increases with mass more than experiment 2a (slope = 6.701e-03, p = 2.245e-09).

Movement Duration by experiment.

Figure 1.1: Movement Duration by experiment.

Movement duration broken up by experiment.

Figure 1.2: Movement duration broken up by experiment.

1.3 Peak Velocity

Table 1.2: Peak Velocity linear models.
Velocity Linear Estimate P-Value Std Error
Circle -1.364e-02 0.000e+00 3.095e-04
Pilot -2.052e-02 0.000e+00 3.331e-04
Arc -1.187e-02 0.000e+00 2.224e-04
All -1.608e-02 0.000e+00 1.810e-04
Table 1.2: Peak Velocity average values (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 0.264±0.076 0.23±0.066 0.393±0.093
3.8 0.235±0.068 0.208±0.06 0.347±0.082
4.7 0.225±0.065 0.201±0.058 0.334±0.079
6.1 0.213±0.061 0.185±0.054 0.315±0.074

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = peakvel_target ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.2779341  0.0173622  16.008  < 2e-16 ***
## factor(targetnum)2 == 0          0.0204180  0.0006711  30.425  < 2e-16 ***
## factor(targetnum)3 == 0          0.0100581  0.0006774  14.847  < 2e-16 ***
## factor(targetnum)4 == 0          0.0234736  0.0006712  34.971  < 2e-16 ***
## eff_mass == 0                   -0.0136629  0.0003421 -39.942  < 2e-16 ***
## factor(exp)pilot == 0            0.1426530  0.0224063   6.367 1.93e-10 ***
## factor(exp)smallt == 0          -0.0349980  0.0245432  -1.426 0.153875    
## eff_mass:factor(exp)pilot == 0  -0.0068836  0.0004385 -15.697  < 2e-16 ***
## eff_mass:factor(exp)smallt == 0  0.0017847  0.0004749   3.758 0.000171 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on peak velocity (slope = -1.366e-02, p = 0.000e+00).

Experiment 2b peak velocity is not different from 2a (p = 1.539e-01).

Experiment 2c peak velocity is significantly greater than 2a (slope = 1.427e-01, p = 1.932e-10).

The interesting thing with these are the interaction effects.

Experiment 2b peak velocity increases with mass more than experiment 2a (slope = 1.785e-03, p = 1.712e-04).

Experiment 2c peak velocity decreases with mass more than experiment 2a (slope = -6.884e-03, p = 0.000e+00).

Peak Velocity by experiment.

Figure 1.3: Peak Velocity by experiment.

Peak velocity broken by experiment.

Figure 1.4: Peak velocity broken by experiment.

1.4 Reaction Time

Table 1.3: Reaction Time linear models.
Reaction Time Linear Estimate P-Value Std Error
Circle 4.645e-03 0.000e+00 3.305e-04
Pilot 5.313e-03 0.000e+00 3.011e-04
Arc 6.401e-03 0.000e+00 3.341e-04
All 5.461e-03 0.000e+00 1.868e-04
Table 1.3: Reaction time average values (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 0.18±0.012 0.204±0.013 0.198±0.012
3.8 0.186±0.013 0.215±0.013 0.207±0.011
4.7 0.189±0.013 0.219±0.013 0.212±0.012
6.1 0.197±0.013 0.228±0.013 0.216±0.011

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 0.1775709  0.0062008  28.637  < 2e-16 ***
## factor(targetnum)2 == 0         -0.0135552  0.0006985 -19.405  < 2e-16 ***
## factor(targetnum)3 == 0         -0.0002042  0.0007051  -0.290 0.772144    
## factor(targetnum)4 == 0         -0.0204404  0.0006987 -29.256  < 2e-16 ***
## eff_mass == 0                    0.0046670  0.0003561  13.108  < 2e-16 ***
## factor(exp)pilot == 0            0.0169967  0.0079800   2.130 0.033179 *  
## factor(exp)smallt == 0           0.0197597  0.0087367   2.262 0.023717 *  
## eff_mass:factor(exp)pilot == 0   0.0006478  0.0004565   1.419 0.155876    
## eff_mass:factor(exp)smallt == 0  0.0017406  0.0004943   3.521 0.000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is an overall effect of mass on reaction_time (slope = 4.667e-03, p = 0.000e+00).

Experiment 2b reaction_time is significantly greater than 2a (slope = 1.976e-02, p = 2.372e-02).

Experiment 2c reaction_time is significantly greater than 2a (slope = 1.700e-02, p = 3.318e-02).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_time increases with mass more than experiment 2a (slope = 1.741e-03, p = 4.294e-04).

Experiment 2c reaction_time did NOT change with mass more than 2a. (p = 1.559e-01).

Reaction Time by experiment.

Figure 1.5: Reaction Time by experiment.

Reaction Time broken by experiment.

Figure 1.6: Reaction Time broken by experiment.

1.4.1 Reaction Velocity

Table 1.4: Reaction Velocity linear models.
Reaction Velocity Linear Estimate P-Value Std Error
Circle 5.994e-05 1.579e-03 1.897e-05
Pilot 8.027e-05 3.342e-02 3.774e-05
Arc 3.659e-05 3.735e-01 4.112e-05
All 5.978e-05 4.338e-03 2.096e-05
Table 1.4: Reaction velocity average values (m/s)
Effective Mass (kg) 2a 2b 2c
2.5 8.951e-04±5.834e-04 -1.554e-04±1.389e-03 -1.621e-04±1.289e-03
3.8 9.981e-04±6.202e-04 -2.193e-04±1.411e-03 -1.224e-04±1.312e-03
4.7 1.051e-03±6.445e-04 5.499e-05±1.494e-03 -3.357e-05±1.272e-03
6.1 1.126e-03±7.045e-04 -7.845e-05±1.556e-03 1.077e-04±1.331e-03

This next stat output shows the a LME with movedur ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanvel ~ factor(targetnum) + eff_mass + 
##     eff_mass * factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 1.161e-03  2.042e-04   5.687 1.30e-08 ***
## factor(targetnum)2 == 0         -1.252e-03  7.837e-05 -15.980  < 2e-16 ***
## factor(targetnum)3 == 0         -4.523e-04  7.912e-05  -5.716 1.09e-08 ***
## factor(targetnum)4 == 0          2.298e-04  7.840e-05   2.931  0.00338 ** 
## eff_mass == 0                    5.310e-05  3.995e-05   1.329  0.18384    
## factor(exp)pilot == 0           -1.179e-03  2.538e-04  -4.645 3.41e-06 ***
## factor(exp)smallt == 0          -1.057e-03  2.761e-04  -3.827  0.00013 ***
## eff_mass:factor(exp)pilot == 0   2.701e-05  5.121e-05   0.527  0.59795    
## eff_mass:factor(exp)smallt == 0 -1.646e-05  5.547e-05  -0.297  0.76671    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on reaction_ (p = 1.838e-01).

Experiment 2b reaction_ is significantly lower than 2a (slope = -1.057e-03, p = 1.298e-04).

Experiment 2c reaction_ is significantly lower than 2a (slope = -1.179e-03, p = 3.408e-06).

The interesting thing with these are the interaction effects.

Experiment 2b reaction_ decreases with mass more than experiment 2a (slope = -1.646e-05, p = 7.667e-01).

Experiment 2c reaction_ did NOT change with mass more than 2a. (p = 5.979e-01).

Reaction by experiment.

Figure 1.7: Reaction by experiment.

Reaction broken by experiment.

Figure 1.8: Reaction broken by experiment.

1.4.2 Reaction Time Algorithm

These next plots are made to try and show the effect of reaciton time algorithms on reaction. Figure 1.9 shows the reaction time by experiment and algorithm. Figure @ref(fig:reactiontanvelalgoplot1} shows the velocity at reaction time by the experiments and algorithms. This plot shows that my algorithm is detecting movement onset at very very low movement speeds, whereas other methods detect it at MUCH higher movement speeds.

Reaction Time Algorithm method.

Figure 1.9: Reaction Time Algorithm method.

Reaction Velocity Algorithm method.

Figure 1.10: Reaction Velocity Algorithm method.

1.5 Endpoint Error

Table 1.5: Miss Distance linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle -3.925e-05 1.486e-01 2.717e-05
Pilot 1.023e-03 0.000e+00 9.391e-05
Arc -1.389e-04 8.788e-05 3.541e-05
All 3.740e-04 0.000e+00 4.370e-05
Table 1.5: Miss Distance average values (cm)
Effective Mass (kg) 2a 2b 2c
2.5 0.623±0.094 0.887±0.141 12.712±0.409
3.8 0.611±0.096 0.831±0.129 13.029±0.423
4.7 0.608±0.099 0.857±0.138 13.107±0.419
6.1 0.605±0.098 0.832±0.133 13.08±0.415

This next stat output shows the a LME with miss_dist ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist ~ factor(targetnum) + eff_mass + eff_mass * 
##     factor(exp) + (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 7.135e-03  2.131e-03   3.348 0.000814 ***
## factor(targetnum)2 == 0         -3.762e-03  1.629e-04 -23.091  < 2e-16 ***
## factor(targetnum)3 == 0          1.503e-03  1.645e-04   9.138  < 2e-16 ***
## factor(targetnum)4 == 0         -3.755e-04  1.630e-04  -2.304 0.021208 *  
## eff_mass == 0                   -5.904e-05  8.305e-05  -0.711 0.477170    
## factor(exp)pilot == 0            1.194e-01  2.748e-03  43.444  < 2e-16 ***
## factor(exp)smallt == 0           2.689e-03  3.009e-03   0.894 0.371434    
## eff_mass:factor(exp)pilot == 0   1.071e-03  1.065e-04  10.059  < 2e-16 ***
## eff_mass:factor(exp)smallt == 0 -8.482e-05  1.153e-04  -0.736 0.461944    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on endpoint error (p = 4.772e-01).

Experiment 2b endpoint error is not different from 2a (p = 3.714e-01).

Experiment 2c endpoint error is significantly greater than 2a (slope = 1.194e-01, p = 0.000e+00).

The interesting thing with these are the interaction effects.

Experiment 2b endpoint error decreases with mass more than experiment 2a (slope = -8.482e-05, p = 4.619e-01).

Experiment 2c endpoint error increases with mass more than experiment 2a (slope = 1.071e-03, p = 0.000e+00).

Miss Distance (cm) by experiment.

Figure 1.11: Miss Distance (cm) by experiment.

Miss Distance (cm) broken by experiment.

(#fig:miss_dist11)Miss Distance (cm) broken by experiment.

1.5.1 Miss Average over trials

Table @ref{tab:missavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.6: Average by mass and experiment.
2a 2b 2c
2.47 0.0062333 0.0088717 0.1272054
3.8 0.0061016 0.0083199 0.1303839
4.7 0.0060759 0.0085774 0.1311127
6.1 0.0060389 0.0083310 0.1308565
Miss Dist Average over trials.

Figure 1.12: Miss Dist Average over trials.

1.5.1.1 Stat Miss Average

cftest(lmer(miss_dist_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        4.815e-03  1.990e-03   2.420 0.015539 *  
## eff_mass == 0           3.745e-04  1.857e-05  20.170  < 2e-16 ***
## trial == 0             -1.174e-06  3.180e-07  -3.693 0.000222 ***
## factor(exp)pilot == 0   1.238e-01  2.566e-03  48.239  < 2e-16 ***
## factor(exp)smallt == 0  2.258e-03  2.811e-03   0.803 0.421737    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.5.2 Miss SD over trials

Table @ref{tab:missvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.7: Average SD by mass and experiment.
2a 2b 2c
2.47 0.0030362 0.0043348 0.0128198
3.8 0.0030910 0.0041096 0.0132033
4.7 0.0031724 0.0043044 0.0134056
6.1 0.0031148 0.0041577 0.0130635

Table @ref{tab:missvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.8: Average Endpoint Error SD for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.0057 0.0045 0.0039 0.0029 0.0028 0.0029 0.003
4.73 kg 0.0065 0.0049 0.0038 0.0036 0.003 0.0033 0.0032
6.99 kg NaN 0.005 0.0042 0.0035 0.0027 0.0026 0.0034
11.50 kg NaN 0.0056 0.0044 0.0034 0.0029 0.0028 0.0033

This next plot (fig @ref{fig:missdistvartplot}) shows the standard deviation of miss distance over the trials for every subject and mass.

Miss Dist SD over trials.

Figure 1.13: Miss Dist SD over trials.

1.5.2.1 Stat Miss Standard Deviation

cftest(lmer(miss_dist_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_dist_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        3.059e-03  6.190e-04   4.942 7.72e-07 ***
## eff_mass == 0           3.233e-05  8.544e-06   3.784 0.000154 ***
## trial == 0             -3.684e-07  1.463e-07  -2.518 0.011812 *  
## factor(exp)pilot == 0   1.010e-02  7.969e-04  12.677  < 2e-16 ***
## factor(exp)smallt == 0  1.081e-03  8.729e-04   1.238 0.215652    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.5.2.2 Metabolics

This next plot (fig @ref{fig:missdistvartplotmet}) shows the standard deviation of miss distance over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Miss Dist SD over trials for metabolic experiment.

Figure 1.14: Miss Dist SD over trials for metabolic experiment.

1.6 Angular Variance

Table 1.9: Miss Distance linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle 9.021e-02 2.331e-01 7.565e-02
Pilot 6.775e-01 7.504e-01 2.130e+00
Arc -4.072e-01 5.259e-01 6.420e-01
All 1.998e-01 8.294e-01 9.270e-01
Table 1.9: Miss Angle Variance average values (deg^2)
Effective Mass (kg) 2a 2b 2c
2.5 2.988±0.375 19.59±4.591 82.775±14.702
3.8 2.551±0.238 15.455±2.954 92.356±23.995
4.7 3.023±0.299 19.224±4.053 89.809±18.937
6.1 3.212±0.267 17.067±3.091 86.145±16.938

This next stat output shows the a LME with missangle ~ target + eff_mass*exp + (1|subj).

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle ~ eff_mass * factor(exp) + (1 | subj), 
##     data = var_data)
## 
## Linear Hypotheses:
##                                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0                 2.55856   16.67940   0.153 0.878086    
## eff_mass == 0                    0.09021    1.74656   0.052 0.958807    
## factor(exp)smallt == 0          17.01325   23.58824   0.721 0.470750    
## factor(exp)pilot == 0           82.32164   21.53302   3.823 0.000132 ***
## eff_mass:factor(exp)smallt == 0 -0.49741    2.47000  -0.201 0.840400    
## eff_mass:factor(exp)pilot == 0   0.58730    2.25480   0.260 0.794505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

There is NOT an overall effect of mass on miss angle variance (p = 9.588e-01).

Experiment 2b miss angle variance is not different from 2a (p = 4.707e-01).

Experiment 2c miss angle variance is significantly greater than 2a (slope = 8.232e+01, p = 1.318e-04).

The interesting thing with these are the interaction effects.

Experiment 2b miss angle variance decreases with mass more than experiment 2a (slope = -4.974e-01, p = 8.404e-01).

Experiment 2c miss angle variance did NOT change with mass more than 2a. (p = 7.945e-01).

Miss Angle Variance (deg^2) by experiment.

Figure 1.15: Miss Angle Variance (deg^2) by experiment.

Miss Angle Variance (deg^2) broken by experiment.

Figure 1.16: Miss Angle Variance (deg^2) broken by experiment.

1.6.1 Angular Miss Average over trials

Table @ref{tab:missangavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.10: Average by mass and experiment.
2a 2b 2c
2.47 0.1001624 1.0104141 4.249243
3.8 0.1962406 0.9631639 3.719996
4.7 0.1278115 1.0994883 3.805261
6.1 0.0842250 0.7822437 3.690864
Miss Angle Average over trials.

Figure 1.17: Miss Angle Average over trials.

1.6.1.1 Stat Miss Angle Average

cftest(lmer(missangle_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        3.591e-01  6.045e-01   0.594   0.5525    
## eff_mass == 0          -6.232e-02  5.811e-03 -10.726  < 2e-16 ***
## trial == 0              2.430e-04  9.952e-05   2.442   0.0146 *  
## factor(exp)pilot == 0   3.822e+00  7.793e-01   4.904 9.38e-07 ***
## factor(exp)smallt == 0  8.500e-01  8.537e-01   0.996   0.3194    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.6.2 Angular Miss standard deviation over trials

Table @ref{tab:missangvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.11: Average by mass and experiment.
2a 2b 2c
2.47 1.662090 3.986924 8.396830
3.8 1.530235 3.645400 8.692422
4.7 1.661973 4.035591 8.750259
6.1 1.712020 3.860505 8.684456

Table @ref{tab:missangvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.12: Average Endpoint Error standard deviation for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 2.0588 2.2745 1.8643 1.5763 1.3719 1.3841 1.5603
4.73 kg 2.5019 2.1617 1.818 1.5901 1.3747 1.5252 1.5685
6.99 kg NaN 2.1953 1.818 1.6125 1.4368 1.2735 1.3828
11.50 kg NaN 2.2009 1.9782 1.6805 1.572 1.4188 1.5063

This next plot (fig @ref{fig:missangvartplot}) shows the standard deviation of angular over the trials for every subject and mass.

Miss Angle standard deviation over trials.

Figure 1.18: Miss Angle standard deviation over trials.

1.6.2.1 Stat Miss Angle Standard Deviation

cftest(lmer(missangle_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = missangle_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                         Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0       1.448e+00  6.790e-01   2.133   0.0330 *  
## eff_mass == 0          2.638e-02  4.982e-03   5.296 1.18e-07 ***
## trial == 0             4.787e-04  8.532e-05   5.610 2.02e-08 ***
## factor(exp)pilot == 0  7.140e+00  8.759e-01   8.152 4.44e-16 ***
## factor(exp)smallt == 0 2.296e+00  9.595e-01   2.393   0.0167 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.6.2.2 Metabolics

This next plot (fig @ref{fig:missangvartplotmet}) shows the standard deviation of miss angle over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Miss angle standard deviation over trials for metabolic experiment.

Figure 1.19: Miss angle standard deviation over trials for metabolic experiment.

1.7 Radial Variance

Table 1.13: Miss Distance Radial Variance (cm^2) linear models.
Miss Distance Linear Estimate P-Value Std Error
Circle -4.307e-03 2.749e-01 3.944e-03
Pilot 2.582e-01 3.343e-03 8.798e-02
Arc -4.993e-03 8.036e-02 2.855e-03
All 1.080e-01 5.990e-03 3.929e-02
Table 1.13: Miss Radial Variance average values (cm^2)
Effective Mass (kg) 2a 2b 2c
2.5 0.2651±0.0148 0.2339±0.0164 1.4368±0.5526
3.8 0.2529±0.0131 0.2227±0.015 1.9259±0.586
4.7 0.25±0.0142 0.2159±0.0153 2.1909±0.4874
6.1 0.2492±0.0208 0.2162±0.0127 2.369±0.471

This next stat output shows the a LME with miss_rad ~ eff_mass*exp + (1|subj).

## NULL

There is NOT an overall effect of mass on miss radial variance (p = 9.515e-01).

Experiment 2b miss radial variance is not different from 2a (p = 9.668e-01).

Experiment 2c miss radial variance is not different from 2a (p = 3.429e-01).

The interesting thing with these are the interaction effects.

Experiment 2b miss radial variance did NOT change with mass more than 2a. (p = 9.945e-01).

Experiment 2c miss radial variance increases with mass more than experiment 2a (slope = 2.625e-01, p = 4.074e-03).

Miss Radial Variance by experiment.

Figure 1.20: Miss Radial Variance by experiment.

Miss Rad Variance (cm^2) broken by experiment.

Figure 1.21: Miss Rad Variance (cm^2) broken by experiment.

1.7.1 Radial Miss Average over trials

Table @ref{tab:missradavgtrialtab} shows the average values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window, then averaged over all points.

Table 1.14: Average by mass and experiment.
2a 2b 2c
2.47 0.0986310 0.0979616 0.0785736
3.8 0.0985490 0.0980965 0.0811442
4.7 0.0990690 0.0981179 0.0826006
6.1 0.0993256 0.0982913 0.0852493
Miss Rad Average over trials.

Figure 1.22: Miss Rad Average over trials.

1.7.1.1 Stat Rad Angle Average

cftest(lmer(miss_rad_avg ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_rad_avg ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        9.531e-02  2.083e-03  45.753  < 2e-16 ***
## eff_mass == 0           8.210e-04  1.478e-05  55.543  < 2e-16 ***
## trial == 0              3.651e-08  2.532e-07   0.144    0.885    
## factor(exp)pilot == 0  -1.623e-02  2.687e-03  -6.041 1.53e-09 ***
## factor(exp)smallt == 0 -7.675e-04  2.944e-03  -0.261    0.794    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.7.2 Radial Miss standard deviation over trials

Table @ref{tab:missradvartrialtab} shows the average standard deviation values for experiment 2a, 2b, and 2c. These are calculated from a 20 trial window standard deviation, then averaged over all points.

Table 1.15: Average standard deviation by mass and experiment.
2a 2b 2c
2.47 0.0050490 0.0047508 0.0069068
3.8 0.0049380 0.0046566 0.0094450
4.7 0.0049295 0.0045833 0.0116504
6.1 0.0048226 0.0045860 0.0127107

Table @ref{tab:missradvartrialtabmet} shows the average standard deviation values for experiment 1.

Table 1.16: Average Endpoint Error standard deviation for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.0087 0.0067 0.0057 0.0047 0.0049 0.0049 0.0057
4.73 kg 0.009 0.0066 0.0054 0.0054 0.0049 0.0053 0.0054
6.99 kg NaN 0.0066 0.0057 0.005 0.0045 0.0044 0.0048
11.50 kg NaN 0.0074 0.0056 0.0049 0.0046 0.0042 0.0048

This next plot (fig @ref{fig:missradvartplot}) shows the standard deviation of radial miss distance over the trials for every subject and mass.

Miss Rad standard deviation over trials.

Figure 1.23: Miss Rad standard deviation over trials.

1.7.2.1 Stat Rad Angle Standard Deviation

cftest(lmer(miss_rad_sd ~ eff_mass + trial + factor(exp) + (1|subj),data=prefpilot))
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = miss_rad_sd ~ eff_mass + trial + factor(exp) + 
##     (1 | subj), data = prefpilot)
## 
## Linear Hypotheses:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0        2.328e-03  1.482e-03   1.570  0.11635    
## eff_mass == 0           6.351e-04  1.688e-05  37.618  < 2e-16 ***
## trial == 0             -4.816e-07  2.891e-07  -1.666  0.09577 .  
## factor(exp)pilot == 0   5.607e-03  1.910e-03   2.935  0.00333 ** 
## factor(exp)smallt == 0 -3.748e-04  2.093e-03  -0.179  0.85785    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

1.7.2.2 Metabolics

This next plot (fig @ref{fig:missradvartplotmet}) shows the standard deviation of miss distance over the trials for every subject, mass, and Speed.

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
Miss Dist standard deviation over trials for metabolic experiment.

Figure 1.24: Miss Dist standard deviation over trials for metabolic experiment.

1.8 Resample Plots

Velocity trajectories by experiment.

Figure 1.25: Velocity trajectories by experiment.

1.9 Preferred Experiment Grouped Plots

Preferred experiment results.

Figure 1.26: Preferred experiment results.

2 Metabolics Experiment

We filtered the metabolic data and removed any trial where the miss distance at endpoint was greater than 10 cm, the movement duration was less than 0.2 seconds, or the reaction time was greater than 0.50 s.This removed 13 out of 15975 original data poitns.

2.0.1 Speed on speed

## Analysis of Variance Table
## 
## Response: movedur
##              Df  Sum Sq Mean Sq    F value Pr(>F)    
## speed         1 1099.40 1099.40 1.0453e+05 <2e-16 ***
## eff_mass2     1    0.01    0.01 6.3430e-01 0.4258    
## Residuals 15959  167.85    0.01                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = movedur ~ speed + eff_mass2 + (1 | subj), data = metdata_factor)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 2.498e-01  8.172e-03  30.571   <2e-16 ***
## speed == 0       1.544e-01  4.760e-04 324.257   <2e-16 ***
## eff_mass2 == 0   5.641e-06  2.371e-04   0.024    0.981    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

2.1 MP Gross

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowergross) ~ log(movedur) + effmass2 + 
##     (1 | subject), data = mpdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   4.561517   0.066021  69.092  < 2e-16 ***
## log(movedur) == 0 -0.766794   0.037690 -20.345  < 2e-16 ***
## effmass2 == 0      0.017373   0.003369   5.156 2.52e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## NULL
Table 2.1: Gross Metabolic power plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 171.9775 ± 18.515 131.625 ± 14.3282 110.1838 ± 5.8343 98.8513 ± 7.9976 105.3988 ± 8.8935 99.835 ± 7.0959 NaN ± NA
4.73 kg 187.4712 ± 17.3187 153.6538 ± 13.0638 126.0213 ± 8.2191 104.4825 ± 6.9769 97.5825 ± 7.3818 97.2367 ± 5.4622 NaN ± NA
6.99 kg NaN ± NA 185.5288 ± 19.5249 140.2988 ± 11.6277 112.705 ± 6.8381 109.9457 ± 8.6896 98.7512 ± 7.5674 93.9237 ± 7.265
11.50 kg NaN ± NA 222.0613 ± 24.3934 155.0838 ± 13.5348 117.4025 ± 10.6555 110.285 ± 10.4558 96.8337 ± 5.2816 92.7812 ± 6.6335
Gross metabolic power.

Figure 2.1: Gross metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.2: Gross metabolic power coefficients.
a only a*subject mass a*effective mass
a 98.2501±3.0512 22.0844±13.6907 101.4027±7.5926
b 0.864±0.4319 0.8593±0.4234 0.8375±0.4215
c 0.8308±0.0998 0.8247±0.0981 0.8548±0.1107
d 5.8254±0.603 5.8562±0.5956 5.8035±0.6061
f null 0.2983±0.1232 -0.0187±0.0411
SSE 120872.749595644 116826.723834405 120743.074844557
AIC 1750.832 1746.4653 1752.6313
BIC 1766.9875 1765.852 1772.0179

2.2 MP net

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(metpowernet) ~ log(movedur) + effmass2 + (1 | 
##     subject), data = mpdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   2.85218    0.23454  12.161  < 2e-16 ***
## log(movedur) == 0 -2.37941    0.16610 -14.326  < 2e-16 ***
## effmass2 == 0      0.04912    0.01485   3.308  0.00094 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.3: Net Metabolic power plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 99.075 ± 17.3755 57.7875 ± 15.0154 36.3125 ± 5.9248 24.9875 ± 6.1351 31.5325 ± 8.1858 27.9333 ± 5.6508 NaN ± NA
4.73 kg 113.7375 ± 18.2929 79.9875 ± 13.8077 52.3875 ± 8.9795 30.8212 ± 5.8168 23.9213 ± 7.2462 24.4667 ± 4.0208 NaN ± NA
6.99 kg NaN ± NA 111.7875 ± 19.9953 65.4 ± 11.9993 37.8638 ± 7.2397 37.7043 ± 7.8668 23.8963 ± 6.5959 19.0538 ± 6.8651
11.50 kg NaN ± NA 150.475 ± 22.0585 83.35 ± 13.048 45.6812 ± 10.4043 38.5625 ± 9.4318 25.0825 ± 5.0728 21.0525 ± 5.3099
Net metabolic power.

Figure 2.2: Net metabolic power.

Parameter estimates are showing as mean +- standard error. The columns are for without the subject mass coefficient, and with a mass coefficient on the effort model. Subj Mass Coef is the subject mass exponent.

The no_mass_coef model is as follows: \[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

The Subject mass model times a1 is as follows: \[ \dot{e} = a*Body Mass^{f}+\frac{bm^c}{T_m^d} \]

The effective mass model times a1 is as follows: \[ \dot{e} = a*Effective\, Mass^{f}+\frac{bm^c}{T_m^d} \]

Table 2.4: Net metabolic power coefficients.
a only a*subject mass a*effective mass
a 24.7227±2.9124 0.1006±0.2368 24.0136±7.0228
b 1.0308±0.467 1.0007±0.4474 1.031±0.4707
c 0.7964±0.0904 0.7942±0.089 0.7962±0.1007
d 5.6574±0.5473 5.7151±0.5413 5.6575±0.5519
f null 1.0939±0.4615 5e-04±0.1585
SSE 105365.400000357 101455.132835216 105365.395173997
AIC 1725.1562 1720.0843 1727.1561
BIC 1741.3117 1739.4709 1746.5428

2.3 MCost Gross

Table 2.5: Gross Metabolic Cost plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 93.3222 ± 8.9748 80.1472 ± 7.2013 82.5764 ± 3.4054 94.0607 ± 9.0851 117.4043 ± 9.7673 125.4443 ± 10.8215 NaN ± NA
4.73 kg 104.3653 ± 7.7764 95.0103 ± 5.6431 96.0467 ± 6.7137 97.5592 ± 7.0411 109.7052 ± 8.5622 123.3466 ± 10.6279 NaN ± NA
6.99 kg NaN ± NA 108.7596 ± 10.3474 95.2653 ± 7.1374 96.7068 ± 6.2899 113.0375 ± 8.3502 120.2383 ± 9.9578 130.8822 ± 10.7193
11.50 kg NaN ± NA 134.6313 ± 12.7635 106.7865 ± 8.1232 101.0186 ± 8.5022 112.9603 ± 9.2217 118.1752 ± 7.0501 128.0428 ± 9.1786
Gross metabolic cost.

Figure 2.3: Gross metabolic cost.

The linear slope of the metabolic minimum is 0.0173807.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.6: Minimum Cost durations for gross metabolic cost.
Effective Mass (kg) Minimum Cost (J) Minimum Cost Duration (s) Preferred Duraiton (s)
a1 2.471 78.44419 0.6613455 0.7638165
a1 3.800 83.41499 0.7032816 0.8299896
a1 4.700 85.98258 0.7249254 0.8559532
a1 6.100 89.24014 0.7523910 0.8902248

2.4 MCost Net

Table 2.7: Net Metabolic Cost plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 53.1932 ± 8.5657 34.0816 ± 8.4267 26.267 ± 3.4663 23.2311 ± 5.6268 33.9323 ± 8.6921 35.0672 ± 7.0593 NaN ± NA
4.73 kg 62.5789 ± 9.018 48.3557 ± 6.9453 39.0854 ± 6.5272 27.9088 ± 5.0761 25.9021 ± 7.7596 31.196 ± 5.3426 NaN ± NA
6.99 kg NaN ± NA 65.0537 ± 11.2371 44.2351 ± 7.8498 32.5745 ± 6.4326 38.6832 ± 7.8991 29.137 ± 8.1055 26.4202 ± 9.651
11.50 kg NaN ± NA 90.9807 ± 11.7824 57.0999 ± 8.418 39.0674 ± 8.6669 38.9813 ± 8.9591 30.4859 ± 6.2224 28.82 ± 7.2275
Net metabolic cost.

Figure 2.4: Net metabolic cost.

The optimal movement durations using the preferred masses are shown below along with the average movement durations.

Table 2.8: Minimum Cost durations for net metabolic cost.
Effective Mass (kg) Minimum Cost (J) Minimum Cost Duration (s) Preferred Duraiton (s)
a1 2.471 25.52908 0.8500727 0.7638165
a1 3.800 27.12511 0.9032332 0.8299896
a1 4.700 27.94902 0.9306663 0.8559532
a1 6.100 28.99388 0.9654625 0.8902248

2.5 Table of Movement Durations

Table 2.9: Movement Duration plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.5486 ± 0.014 0.6202 ± 0.0211 0.7576 ± 0.0325 0.951 ± 0.0419 1.1227 ± 0.0476 1.2528 ± 0.04 NaN ± NA
4.73 kg 0.5644 ± 0.0145 0.6295 ± 0.0219 0.7677 ± 0.0355 0.9386 ± 0.0381 1.1305 ± 0.0416 1.2593 ± 0.0459 NaN ± NA
6.99 kg NaN ± NA 0.5921 ± 0.011 0.6819 ± 0.007 0.8569 ± 0.0082 1.0306 ± 0.0152 1.2143 ± 0.0205 1.3931 ± 0.0269
11.50 kg NaN ± NA 0.6114 ± 0.0113 0.6931 ± 0.0115 0.8638 ± 0.0102 1.0304 ± 0.0163 1.2184 ± 0.0144 1.38 ± 0.013

2.6 Endpoint Error

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_dist) ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  -5.529646   0.058862  -93.94   <2e-16 ***
## log(movedur) == 0 -0.937237   0.017751  -52.80   <2e-16 ***
## eff_mass2 == 0     0.021596   0.001683   12.83   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.10: Endpoitn Error plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.0118 ± 3e-04 0.0084 ± 2e-04 0.0075 ± 2e-04 0.0056 ± 1e-04 0.0047 ± 1e-04 0.0046 ± 1e-04 0.0052 ± 3e-04
4.73 kg 0.0129 ± 4e-04 0.0094 ± 2e-04 0.0075 ± 1e-04 0.0065 ± 1e-04 0.0052 ± 1e-04 0.005 ± 1e-04 0.0055 ± 3e-04
6.99 kg NaN ± NA 0.0105 ± 2e-04 0.0088 ± 2e-04 0.0065 ± 1e-04 0.0051 ± 1e-04 0.0044 ± 1e-04 0.005 ± 1e-04
11.50 kg NaN ± NA 0.0122 ± 2e-04 0.0092 ± 2e-04 0.0067 ± 1e-04 0.0053 ± 1e-04 0.0045 ± 1e-04 0.0049 ± 1e-04 
## `geom_smooth()` using formula 'y ~ x'
Endpoint Error.

Figure 2.5: Endpoint Error.

2.7 Angle Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(missangle) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0   0.724150   0.111106   6.518 7.14e-11 ***
## log(movedur) == 0 -1.140515   0.074456 -15.318  < 2e-16 ***
## eff_mass == 0      0.017424   0.006883   2.532   0.0114 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.11: Miss Angle Variance plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 1.1816±,0.2404 0.8386±,0.1829 0.7531±,0.1503 0.5641±,0.1087 0.4743±,0.1047 0.4589±,0.1059 0.5233±,0.1061
4.73 kg 1.2879±,0.2579 0.9431±,0.1916 0.7494±,0.1427 0.6479±,0.1403 0.5246±,0.1151 0.5009±,0.1142 0.547±,0.1099
6.99 kg ±, 1.0496±,0.205 0.8785±,0.1597 0.652±,0.1344 0.511±,0.1173 0.4353±,0.0963 0.4983±,0.1196
11.50 kg ±, 1.2156±,0.2198 0.9214±,0.1697 0.6676±,0.1355 0.53±,0.1126 0.452±,0.101 0.493±,0.1126 
## `geom_smooth()` using formula 'y ~ x'
Angular miss variance.

Figure 2.6: Angular miss variance.

2.8 Radial Endpoint Variance

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = log(miss_rad) ~ log(movedur) + eff_mass + (1 | 
##     subj), data = c)
## 
## Linear Hypotheses:
##                     Estimate Std. Error  z value Pr(>|z|)    
## (Intercept) == 0  -10.559873   0.086527 -122.041   <2e-16 ***
## log(movedur) == 0  -1.000083   0.070358  -14.214   <2e-16 ***
## eff_mass == 0      -0.006928   0.006506   -1.065    0.287    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.12: Radial Endpoint Variance plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.3286±,0.0772 0.2452±,0.0943 0.212±,0.056 0.1659±,0.0119 0.1802±,0.0322 0.1666±,0.0096 0.1983±,0.0012
4.73 kg 0.3244±,0.0778 0.2426±,0.0473 0.1943±,0.0302 0.1928±,0.0334 0.1793±,0.023 0.1752±,0.012 0.183±,0.0184
6.99 kg ±, 0.2456±,0.0572 0.2012±,0.0684 0.1834±,0.0723 0.1603±,0.0278 0.1578±,0.014 0.1647±,0.0191
11.50 kg ±, 0.2745±,0.0397 0.1985±,0.013 0.1776±,0.0235 0.1613±,0.0264 0.1564±,0.0164 0.1619±,0.0177 
## `geom_smooth()` using formula 'y ~ x'
Radial miss variance.

Figure 2.7: Radial miss variance.

2.9 Reaction Time

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ log(movedur) + eff_mass2 + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  0.1585730  0.0071557   22.16   <2e-16 ***
## log(movedur) == 0 0.0530319  0.0012279   43.19   <2e-16 ***
## eff_mass2 == 0    0.0023967  0.0001164   20.59   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = reaction_tanv ~ movedur + eff_mass2 + (1 | subj), 
##     data = metdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.0924072  0.0072719   12.71   <2e-16 ***
## movedur == 0     0.0643985  0.0014023   45.92   <2e-16 ***
## eff_mass2 == 0   0.0023962  0.0001155   20.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)
Table 2.13: Reaction time plus/minus standard error for the metabolic experiment
Speed = 1 Speed = 2 Speed = 3 Speed = 4 Speed = 5 Speed = 6 Speed = 7
2.73 kg 0.1123 ± 0.0028 0.1268 ± 0.002 0.1401 ± 0.0019 0.1547 ± 0.0017 0.1661 ± 0.0018 0.1757 ± 0.0021 0.1931 ± 0.0042
4.73 kg 0.1325 ± 0.0027 0.1344 ± 0.002 0.1445 ± 0.0019 0.1623 ± 0.0016 0.1787 ± 0.0017 0.1922 ± 0.0018 0.2129 ± 0.0051
6.99 kg NaN ± NA 0.137 ± 0.002 0.1489 ± 0.0018 0.1671 ± 0.0018 0.1759 ± 0.0018 0.1938 ± 0.0019 0.2108 ± 0.0022
11.50 kg NaN ± NA 0.1446 ± 0.002 0.157 ± 0.0017 0.1699 ± 0.0019 0.1874 ± 0.0017 0.2021 ± 0.0019 0.2259 ± 0.0023 
## `geom_smooth()` using formula 'y ~ x'
Reaction time in metabolic experiment.

Figure 2.8: Reaction time in metabolic experiment.

2.10 Metabolic results plot

Metabolic experiment results.

Figure 2.9: Metabolic experiment results.

3 Effort models

We compute 4 effort models here. Gross metabolics, net metabolics, and sum of torque squared (experimentally calculated and calcualted from minimum jerk). Net and gross metabolics have been addressed before, here we add sum of torque squared.

Sum of torque sqaured is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power but without the a parameter.

\[ \dot{e} = \frac{bm^c}{T_m^d} \]

The parameters fit for the effort models are shown in table @ref(tab:effort_prarms).

3.1 Torque Squared

Sum of torque squared fits from the data

Figure 3.1: Sum of torque squared fits from the data

3.2 Effort model parameters

This table shows a summary of all the parameters that were fitted in the effort models. SSE, AIC, and BIC can be found in their respective sections.

Table 3.1: Parameters fit in the effort models.
Net Metabolics Gross Metabolics Torque\(^2\) Torque\(^2\) minjerk
a0 73.3259±3.6041 73.3259±3.6041 0 0
a 24.0346 ± 2.9124 98.2501 ± 3.0512 0 0
b 1.0308 ± 0.467 0.864 ± 0.4319 0.0416 ± 0.0079 0.2885 ± 0.0429
c 0.7964 ± 0.0904 0.8308 ± 0.0998 2.1339 ± 0.0728 1.6071 ± 0.054
d 5.6574 ± 0.5473 5.8254 ± 0.603 3.4951 ± 0.1229 1.3379 ± 0.0249
AIC 1725.15615301424 1750.8320060654 9611.79628744657 35100.9080475733
BIC 1741.31169609851 1766.98754914967 9632.60990953091 35125.7853519489

3.2.1 Torque squared models with offset not forced to 0

Sum of torque sqaured is calcualted from the data and simulated minimum jerk profiles and then fit to an effort model like net metabolic and gross metabolic power. In these we allowed \(a\) to be fit to see if it would predict a 0 offset.

\[ \dot{e} = a+\frac{bm^c}{T_m^d} \]

This table shows the confident intervals on the torque with \(a\) model. The probability of \(a\) (\(a_1\)) being greater than 0 is 4.990231110^{-4}.

Table 3.2: Confidence intervals for torque squared model.
2.5% 97.5%
a1 -2.6747330 -0.9462295
a2 0.0553365 0.1392793
a3 1.7512603 2.0645923
a4 2.9486703 3.4315542

4 Probablity Modeling

The probability function for the 2a is: \[ ln\left(\frac{P_i}{1-P_i}\right) = \beta_0 + \beta_2 x_2 \] Which leads to \[ P(Success|T) = \frac{1}{1+e^{-(\beta_0) - (\beta_2)T}} \] Mass is removed from this probability as according to the model it is insignificant. Duration nad mass alos condound here, so we only use duration. I leave it \(\beta_2\) because that is more similar to the glm with mass from experiement 1.

We then use this function to first fit an inverse logit to experiment 2a and 2b. We then use the criteria for success and fit the same inverse logit function but using the data from experiment 1.

4.1 Probability of sucess in just 2a and 2b without 1

The following table shows the beta coefficients for the inverse logit function only predicting from experiment 2a and 2b.

Table 4.1: Beta coefficient for the inverse logit function to predict probability of success.
2a 2b
\(\beta_0\) 2.5791 ± 0.469 1.1985 ± 0.174
\(\beta_2\) 1.6285 ± 0.575 0.4219 ± 0.193

Using these functions we can then predict the probability of success as a fraction of success given the data and using the logit model. The following table shows this for experiment 2a and 2b.

Table 4.2: Success probabilities for experiment 2a and 2b. Also predicted from glm fitted using data from 2a and 2b
2a Predicted 2a 2b Predicted 2b
2.47 0.9782 0.9786 0.8110 0.8243
3.8 0.9839 0.9807 0.8537 0.8278
4.7 0.9779 0.9815 0.8167 0.8293
6.1 0.9815 0.9825 0.8318 0.8324

4.1.1 2a and 2b GLM probability plots

The plot below shows the fits of the glm’s fitted to only data from experiment 2a and 2b. Unfortunately, these glm’s don’t seem to have the same behavior as data fitted to experiment 1 of dropping off to 0 at faster speeds. This is probably due to the lack of really fast or really slow trials so it just predicts a flat line essentially.

Probability of success with glm fitted to experiment 2a and 2b data.

Figure 4.1: Probability of success with glm fitted to experiment 2a and 2b data.

4.1.2 Success variability over the experiment

4.1.2.1 2a

The following plot shows the average success (20 trials) of over the trial for experiment 2a.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_avg ~ eff_mass + trial + (1 | subj), data = prefdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  9.805e-01  6.389e-03 153.454  < 2e-16 ***
## eff_mass == 0     2.714e-04  2.550e-04   1.064    0.287    
## trial == 0       -1.383e-05  2.952e-06  -4.685 2.79e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

The following plot shows the variability (20 trials) of over the trial for experiment 2a.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_sd ~ eff_mass + trial + (1 | subj), data = prefdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 6.782e-02  2.040e-02   3.324 0.000887 ***
## eff_mass == 0    5.902e-04  8.475e-04   0.696 0.486201    
## trial == 0       3.928e-05  9.812e-06   4.003 6.25e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.2.2 2b

The following plot shows the average success (20 trials) of over the trial for experiment 2b.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_avg ~ eff_mass + trial + (1 | subj), data = smalltdata)
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 8.012e-01  3.445e-02  23.260  < 2e-16 ***
## eff_mass == 0    3.889e-03  8.009e-04   4.856 1.20e-06 ***
## trial == 0       7.673e-05  1.857e-05   4.133 3.58e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

The following plot shows the variability (20 trials) of over the trial for experiment 2b.

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_sd ~ eff_mass + trial + (1 | subj), data = smalltdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  3.130e-01  3.975e-02   7.873 3.55e-15 ***
## eff_mass == 0     1.996e-03  8.572e-04   2.329  0.01988 *  
## trial == 0       -5.311e-05  1.987e-05  -2.672  0.00753 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.3 Statistics on probability of success 2a

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success ~ eff_mass + (1 | subj), data = aggregate(success ~ 
##     eff_mass + subj, prefdata, mean))
## 
## Linear Hypotheses:
##                   Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.9781917  0.0089704 109.046   <2e-16 ***
## eff_mass == 0    0.0001357  0.0014250   0.095    0.924    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.1.4 Statistics on probability of success 2b

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success ~ eff_mass + (1 | subj), data = aggregate(success ~ 
##     eff_mass + subj, smalltdata, mean))
## 
## Linear Hypotheses:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0 0.803251   0.046611  17.233   <2e-16 ***
## eff_mass == 0    0.004996   0.007143   0.699    0.484    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.2 Probability of success using experiment 1

This table shows the beta coefficients when using an inverse logit on experiment 1 trying to predict 2a and 2b.

Table 4.3: Beta coefficient for the inverse logit function to predict probability of success.
2a 2b
\(\beta_0\) -1.4458 ± 0.125 -2.5804 ± 0.077
\(\beta_1\) -0.0966 ± 0.008 -0.0641 ± 0.006
\(\beta_2\) 5.8758 ± 0.188 4.8391 ± 0.1

This plot only includes movement durations that are seen in the metabolic experiment. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Figure 4.2: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This plot includes low and high movement durations to show that the functions converge to 0 and 1 probability respectively.

Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

Figure 4.3: Probability of success given movement duration and mass. The black vertical bars show the range of durations for the 2a preferred exerpiement. The red vertical bars show the range of durations for the smallt target.

This next table shows the movement durations for experiment 2a and 2b, the probability of success from the experiment, along with the probability of success from the logistic regression. The last row is the mean probability.

2a Movedur 2a Exp Prob 2a Pred Prob 2b Movedur 2b Exp Prob 2b Pred Prob
2.47 0.7638 0.9782 0.9429 0.8226 0.8110 0.7759
3.80 0.8300 0.9839 0.9554 0.8813 0.8537 0.8086
4.70 0.8560 0.9779 0.9581 0.9051 0.8167 0.8173
6.10 0.8902 0.9815 0.9607 0.9588 0.8318 0.8414
Mean NaN 0.9804 0.9543 NaN 0.8283 0.8108

4.2.1 Success Over trials

4.2.1.1 Average Reward over trials

Reward average over trials for metabolic experiment.

Figure 4.4: Reward average over trials for metabolic experiment. 

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_2a_avg ~ eff_mass2 + trial + speed + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error z value Pr(>|z|)    
## (Intercept) == 0  7.275e-01  1.971e-02  36.908  < 2e-16 ***
## eff_mass2 == 0   -7.505e-03  2.675e-04 -28.057  < 2e-16 ***
## trial == 0        6.352e-05  1.768e-05   3.593 0.000327 ***
## speed == 0        5.419e-02  5.805e-04  93.348  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.2.1.2 Reward Variance over trials

Reward standard deviation over trials for metabolic experiment.

Figure 4.5: Reward standard deviation over trials for metabolic experiment. 

## 
##   Simultaneous Tests for General Linear Hypotheses
## 
## Fit: lmer(formula = success_2a_sd ~ eff_mass2 + trial + speed + (1 | 
##     subj), data = metdata)
## 
## Linear Hypotheses:
##                    Estimate Std. Error  z value Pr(>|z|)    
## (Intercept) == 0  4.240e-01  2.388e-02   17.754  < 2e-16 ***
## eff_mass2 == 0    9.910e-03  3.083e-04   32.148  < 2e-16 ***
## trial == 0       -1.281e-04  2.037e-05   -6.289  3.2e-10 ***
## speed == 0       -7.407e-02  6.690e-04 -110.716  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Univariate p values reported)

4.3 Predicting movedur off of probability

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.9498. The table below shows the predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0038674.

Table 4.4: Predicted movement durations for the 2a given probability of: 0.9498
Effective Mass (kg) Predicted Duration Preferred Duration
2.47 0.787 0.764
3.8 0.809 0.83
4.7 0.824 0.856
6.1 0.847 0.89

The probability of reward that minimizes the error of predicted movement durations for the 2a experiment is 0.811. The table below shows hte predicted movement durations and the expected movement durations. The SSE of this prediction is 0.0255866.

Table 4.5: Predicted movement durations for the 2b given probability of: 0.811
Effective Mass (kg) Predicted Duration Preferred Duration
2.47 0.867 0.823
3.8 0.885 0.881
4.7 0.897 0.905
6.1 0.916 0.959

5 Utility Modeling

5.1 Individual Utility

This plot below shows individual subjects and their utility fits. This uses gross metabolics as the effort term.

The average fitted \(\alpha\) value was 50.3353.

Utility fits by subject.

Figure 5.1: Utility fits by subject.

5.2 Utility Code

5.2.1 Combined utility code

5.3 Table for the coefficients in Utility Modeling

We next fitted a utility model by altering \(\alpha\) to try and predict the movement durations seen in 2a,b,c.

The utility function that is fit for these next plots is below. \(T_r\) and \(T_m\) are the reaction time and movement duration. \(P(R|m,t)\) is determined from the section above, probability alpha modeling. \(a\), \(b\), \(c\), \(d\) are determined from the metabolic data. Resting rate is shown by \(a_0\), and \(a_0\) = 73.527. The parameters a, b, c, and d are shown in 3.1.

\[J = \frac{\alpha P(R|m,T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\] Ideally the probability function has an effect of mass in it, but for the following results we use the glm from experiement 2a/2b to fit \(\alpha\), which leads to the probability function only including a term of time.

\[J = \frac{\alpha P(R|T_m) -\left( a_0 T_r + a T_m + \frac{bm^c}{T_m^d} \right)}{T_r+T_m}\]

\(T_r\) and \(T_m\) are the reaction time and movement duration. Using the values from experiment 2a,b,c, we can optimize the error of the prediction by altering \(\alpha\).

The tables below show the movement durations (@ref{tab:utilmovedurstab}), reaction time (@ref{rab:utilreacttimestab}).

Table 5.1: Movement durations by experiement and effective mass used in the Utility model
2a 2b 2c
2.47 kg 0.764 0.823 0.632
3.80 kg 0.830 0.881 0.703
4.70 kg 0.856 0.905 0.741
6.10 kg 0.890 0.959 0.781
Table 5.2: Reaction times by experiement and effective mass used in the Utility model
2a 2b 2c
2.47 kg 0.180 0.204 0.198
3.80 kg 0.186 0.215 0.207
4.70 kg 0.189 0.219 0.212
6.10 kg 0.197 0.228 0.216

5.4 Experimental Utility Fits

5.4.1 2a Alpha

Table (5.3) shows the fitted values for alpha given the specific utility model and the parameters fit previously. These are only for experiment 2a.

This table (5.3) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2a}).

Table 5.3: Preferred duration and predicted durations for each model.
2a Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 61.2912 43.5239 22.1808 27.3508
2.47 0.7638 0.8543 0.6613 0.767 0.767 0.49 0.06
4.73 0.83 0.9078 0.7033 0.825 0.825 0.7 0.21
6.99 0.856 0.9353 0.7249 0.855 0.854 0.84 0.44
11.50 0.8902 0.9703 0.7524 0.895 0.892 1.05 1.16
SSE 0 2.695e-02 6.272e-02 5.874e-05 4.200e-05 1.177e-01 1.126e+00

The probability of success for utility in experiement 2a using the optimized alpha value are shown below.

Table 5.4: Probability of success used in utility modeling when fitting alpha, Expirement 2a.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.47 0.9787132 0.9787132 0.9669794 0.9356420
3.8 0.9805946 0.9805946 0.9763173 0.9488775
4.7 0.9815028 0.9814732 0.9810541 0.9642782
6.1 0.9826491 0.9825656 0.9864674 0.9886618

5.4.2 2b Alpha

Table (5.5) shows the fitted values for alpha given the specific utility model and the parameters fit previously. These are only for experiment 2b.

This table (5.3) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.5: Preferred duration and predicted durations for each model.
2b Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 62.0902 37.28 28.7265 38.5367
2.47 0.8226 0.8543 0.6613 0.816 0.82 0.51 0.05
4.73 0.8813 0.9078 0.7033 0.88 0.881 0.75 0.17
6.99 0.9051 0.9353 0.7249 0.913 0.913 0.91 0.36
11.50 0.9588 0.9703 0.7524 0.957 0.953 1.17 1.14
SSE 0 2.749e-03 1.328e-01 1.111e-04 1.033e-04 1.596e-01 1.433e+00

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.6: Probability of success used in utility modeling when fitting alpha, Expirement 2b.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.47 0.8238718 0.8241165 0.8043481 0.7719953
3.8 0.8277559 0.8278160 0.8197945 0.7807843
4.7 0.8297320 0.8297320 0.8295531 0.7941962
6.1 0.8323387 0.8321030 0.8445083 0.8428389

5.4.3 2c Alpha

Table (5.7) shows the fitted values for alpha given the specific utility model and the parameters fit previously. These are only for experiment 2c.

This table (5.7) shows the \(\alpha\) value, predicted durations for the models, and the SSE between that and the experimental data. The SSE for all these models is shown in detail later (section @ref{SSE2b}).

Table 5.7: Preferred duration and predicted durations for each model.
2c Experiment Net Metabolic Power Gross Metabolic power Utility (Net Power) Utility (Gross Power Torque\(^2\) Torque\(^2\) minjerk
Alpha 0 0 0 112.1505 95.6647 26.8914 24.6437
2.47 0.6316 0.8543 0.6613 0.663 0.658 0.42 0.05
4.73 0.7033 0.9078 0.7033 0.713 0.708 0.6 0.14
6.99 0.7412 0.9353 0.7249 0.74 0.734 0.72 0.28
11.50 0.7811 0.9703 0.7524 0.774 0.767 0.91 0.87
SSE 0 1.649e-01 1.972e-03 1.132e-03 9.692e-04 7.251e-02 8.762e-01

The probability of success for utility in experiement 2b using the optimized alpha value are shown below.

Table 5.8: Probability of success used in utility modeling when fitting alpha, Expirement 2c.
Utility Net Utility Gross Utility Torque Utility Torque Mj
2.47 1 1 1 1
3.8 1 1 1 1
4.7 1 1 1 1
6.1 1 1 1 1

5.5 2a and 2b Combined Utility fits

This section analysis fits one \(\alpha\) value to experiment 2a and 2b at the same time. These next tables show the movement durations, predicted movement durations, the fitted alpha values, and the probabilities of success. The \(\alpha\) value for 2a and 2b are fit at once, so it is the same. 2c has its own \(\alpha\) value.

The \(\alpha\) value fitted here is 40.1149594. The SSE for experiment 2a/2b when using one alpha is 1.201e-03. The SSE for experiment 2c is 9.692e-04. The total SSE for all 3 is 2.170e-03.

Table 5.9: Experimental and predicted movement durations for the experiments.
2a Exp 2a pred 2b Exp 2b pred 2c Exp 2c pred
2.47 0.7638165 0.779 0.8226259 0.810 0.6316043 0.658
3.8 0.8299896 0.837 0.8812989 0.870 0.7032684 0.708
4.7 0.8559532 0.867 0.9051184 0.902 0.7412180 0.734
6.1 0.8902248 0.905 0.9588485 0.942 0.7810693 0.767
Table 5.10: Probabilites of success for the experiments.
2a 2b 2c
2.47 0.9791 0.8235 1
3.8 0.9810 0.8272 1
4.7 0.9819 0.8291 1
6.1 0.9829 0.8315 1
Table 5.11: Alpha values fitted to experiment 2a/2b, and a seperate alpha for 2c.
2a 2b 2c
lpha 40.115 40.115 95.665
Utility fits across experiments.

Figure 5.2: Utility fits across experiments.

5.6 2a Durations

5.6.1 MOdel Plotting Function

5.6.2 DF Creation

5.6.3 Peak Velocity Plotting

5.6.4 SSE of models - Exp 2a

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure 5.2.

5.6.4.1 Absolute

This table shows the SSE for the 2a movement duration and peak velocity predictions.

Table 5.12: Exp 2a - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 3.867e-03 -2.58e+01 -2.64e+01 7.421e-04 -3.24e+01 -3.30e+01
SSE.3 Met Cost Gross 6.272e-02 -1.46e+01 -1.52e+01 3.904e-03 -2.57e+01 -2.63e+01
SSE.4 Met Cost Net 2.695e-02 -1.80e+01 -1.86e+01 3.711e-03 -2.59e+01 -2.65e+01
SSE.5 Torque^2 1.177e-01 -1.21e+01 -1.27e+01 1.641e-02 -2.00e+01 -2.06e+01
SSE.7 Utility Gross 4.200e-05 -4.19e+01 -4.31e+01 4.580e-04 -3.23e+01 -3.35e+01
SSE.9 Utility Net 5.874e-05 -4.05e+01 -4.17e+01 4.647e-04 -3.22e+01 -3.35e+01
SSE.10 Utility Gross Combined Alpha 6.200e-04 -3.11e+01 -3.23e+01 7.443e-04 -3.04e+01 -3.16e+01
SSE.11 Utility Net Combined Alpha 6.668e-05 -4.00e+01 -4.12e+01 4.246e-04 -3.26e+01 -3.38e+01

5.6.4.2 Normalized

Table 5.13: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.683e-02 -1.99e+01 -2.05e+01 3.270e-02 -1.72e+01 -1.78e+01
SSE.3 Met Cost Gross 1.914e-03 -2.86e+01 -2.92e+01 1.153e-02 -2.14e+01 -2.20e+01
SSE.4 Met Cost Net 2.137e-03 -2.81e+01 -2.88e+01 1.197e-02 -2.12e+01 -2.19e+01
SSE.5 Torque^2 1.425e+00 -2.13e+00 -2.74e+00 2.234e-01 -9.54e+00 -1.02e+01
SSE.7 Utility Gross 1.795e-04 -3.60e+01 -3.73e+01 6.631e-03 -2.16e+01 -2.28e+01
SSE.9 Utility Net 1.580e-04 -3.66e+01 -3.78e+01 6.235e-03 -2.19e+01 -2.31e+01
SSE.10 Utility Gross Combined Alpha 2.211e-04 -3.52e+01 -3.64e+01 6.845e-03 -2.15e+01 -2.27e+01
SSE.11 Utility Net Combined Alpha 1.517e-04 -3.67e+01 -3.79e+01 6.167e-03 -2.19e+01 -2.31e+01

5.6.5 2a Modeling Plot

Modeling Results

Figure 5.3: Modeling Results

5.6.6 SSE of models - Exp 2a to 2b

5.6.6.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.14: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 2.559e-02 -1.82e+01 -1.88e+01 2.639e-03 -2.73e+01 -2.79e+01
SSE.3 Met Cost Gross 1.328e-01 -1.16e+01 -1.22e+01 1.372e-02 -2.07e+01 -2.13e+01
SSE.4 Met Cost Net 2.749e-03 -2.71e+01 -2.77e+01 1.733e-04 -3.82e+01 -3.88e+01
SSE.5 Torque^2 1.561e-01 -1.10e+01 -1.16e+01 2.746e-02 -1.79e+01 -1.85e+01
SSE.7 Utility Gross 1.335e-02 -1.88e+01 -2.00e+01 1.547e-03 -2.74e+01 -2.87e+01
SSE.9 Utility Net 1.285e-02 -1.90e+01 -2.02e+01 1.503e-03 -2.75e+01 -2.88e+01
SSE.10 Utility Gross Combined Alpha 8.218e-03 -2.08e+01 -2.20e+01 1.084e-03 -2.89e+01 -3.01e+01
SSE.11 Utility Net Combined Alpha 1.377e-02 -1.87e+01 -1.99e+01 1.586e-03 -2.73e+01 -2.86e+01

5.6.6.2 Normalized

Table 5.15: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.270e-02 -2.10e+01 -2.16e+01 0.000e+00 -Inf -Inf
SSE.3 Met Cost Gross 8.598e-04 -3.18e+01 -3.24e+01 0.000e+00 -Inf -Inf
SSE.4 Met Cost Net 1.001e-03 -3.12e+01 -3.18e+01 0.000e+00 -Inf -Inf
SSE.5 Torque^2 1.460e+00 -2.03e+00 -2.65e+00 0.000e+00 -Inf -Inf
SSE.7 Utility Gross 1.982e-04 -3.56e+01 -3.69e+01 0.000e+00 -Inf -Inf
SSE.9 Utility Net 2.290e-04 -3.51e+01 -3.63e+01 0.000e+00 -Inf -Inf
SSE.10 Utility Gross Combined Alpha 1.855e-04 -3.59e+01 -3.71e+01 0.000e+00 -Inf -Inf
SSE.11 Utility Net Combined Alpha 2.408e-04 -3.49e+01 -3.61e+01 0.000e+00 -Inf -Inf

5.6.7 SSE of models - Exp 2a to 2c

5.6.7.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.16: Exp 2c - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.653e-02 -1.58e+01 -1.64e+01 5.754e-02 -1.50e+01 -1.56e+01
SSE.3 Met Cost Gross 1.972e-03 -2.85e+01 -2.91e+01 2.861e-02 -1.78e+01 -1.84e+01
SSE.4 Met Cost Net 1.649e-01 -1.08e+01 -1.14e+01 8.275e-02 -1.35e+01 -1.41e+01
SSE.5 Torque^2 1.021e-01 -1.27e+01 -1.33e+01 3.730e-02 -1.67e+01 -1.73e+01
SSE.7 Utility Gross 5.818e-02 -1.29e+01 -1.41e+01 6.069e-02 -1.28e+01 -1.40e+01
SSE.9 Utility Net 5.908e-02 -1.29e+01 -1.41e+01 6.090e-02 -1.27e+01 -1.40e+01
SSE.10 Utility Gross Combined Alpha 7.079e-02 -1.21e+01 -1.34e+01 6.403e-02 -1.25e+01 -1.38e+01
SSE.11 Utility Net Combined Alpha 5.715e-02 -1.30e+01 -1.42e+01 6.036e-02 -1.28e+01 -1.40e+01

5.6.7.2 Normalized

Table 5.17: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.905e-02 -1.56e+01 -1.62e+01 0.000e+00 -Inf -Inf
SSE.3 Met Cost Gross 1.829e-02 -1.95e+01 -2.02e+01 0.000e+00 -Inf -Inf
SSE.4 Met Cost Net 1.899e-02 -1.94e+01 -2.00e+01 0.000e+00 -Inf -Inf
SSE.5 Torque^2 1.213e+00 -2.77e+00 -3.39e+00 0.000e+00 -Inf -Inf
SSE.7 Utility Gross 1.047e-02 -1.98e+01 -2.10e+01 0.000e+00 -Inf -Inf
SSE.9 Utility Net 9.758e-03 -2.01e+01 -2.13e+01 0.000e+00 -Inf -Inf
SSE.10 Utility Gross Combined Alpha 1.080e-02 -1.97e+01 -2.09e+01 0.000e+00 -Inf -Inf
SSE.11 Utility Net Combined Alpha 9.647e-03 -2.01e+01 -2.13e+01 0.000e+00 -Inf -Inf

5.7 2b Durations

5.7.1 DF Creation

5.7.2 Peak Velocity Plotting

5.7.3 SSE of models - Exp 2b

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure 5.2.

5.7.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 5.18: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 2.559e-02 -1.82e+01 -1.88e+01 2.639e-03 -2.73e+01 -2.79e+01
SSE.3 Met Cost Gross 1.328e-01 -1.16e+01 -1.22e+01 1.372e-02 -2.07e+01 -2.13e+01
SSE.4 Met Cost Net 2.749e-03 -2.71e+01 -2.77e+01 1.733e-04 -3.82e+01 -3.88e+01
SSE.5 Torque^2 1.561e-01 -1.10e+01 -1.16e+01 2.746e-02 -1.79e+01 -1.85e+01
SSE.7 Utility Gross 1.033e-04 -3.83e+01 -3.95e+01 1.743e-04 -3.62e+01 -3.74e+01
SSE.9 Utility Net 1.111e-04 -3.80e+01 -3.92e+01 1.571e-04 -3.66e+01 -3.78e+01
SSE.10 Utility Gross Combined Alpha 8.218e-03 -2.08e+01 -2.20e+01 1.084e-03 -2.89e+01 -3.01e+01
SSE.11 Utility Net Combined Alpha 1.377e-02 -1.87e+01 -1.99e+01 1.586e-03 -2.73e+01 -2.86e+01

5.7.3.2 Normalized

Table 5.19: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.270e-02 -2.10e+01 -2.16e+01 2.639e-02 -1.81e+01 -1.87e+01
SSE.3 Met Cost Gross 8.598e-04 -3.18e+01 -3.24e+01 8.069e-03 -2.28e+01 -2.34e+01
SSE.4 Met Cost Net 1.001e-03 -3.12e+01 -3.18e+01 8.438e-03 -2.26e+01 -2.33e+01
SSE.5 Torque^2 1.460e+00 -2.03e+00 -2.65e+00 2.415e-01 -9.23e+00 -9.84e+00
SSE.7 Utility Gross 1.935e-04 -3.57e+01 -3.70e+01 4.229e-03 -2.34e+01 -2.46e+01
SSE.9 Utility Net 4.480e-04 -3.24e+01 -3.36e+01 3.081e-03 -2.47e+01 -2.59e+01
SSE.10 Utility Gross Combined Alpha 1.855e-04 -3.59e+01 -3.71e+01 4.280e-03 -2.34e+01 -2.46e+01
SSE.11 Utility Net Combined Alpha 2.408e-04 -3.49e+01 -3.61e+01 3.709e-03 -2.39e+01 -2.52e+01

5.7.4 2b Modeling Plot

Modeling Results

Figure 5.4: Modeling Results

5.7.5 SSE of models - Exp 2b to 2a

5.7.5.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.20: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 3.867e-03 -2.58e+01 -2.64e+01 7.421e-04 -3.24e+01 -3.30e+01
SSE.3 Met Cost Gross 6.272e-02 -1.46e+01 -1.52e+01 3.904e-03 -2.57e+01 -2.63e+01
SSE.4 Met Cost Net 2.695e-02 -1.80e+01 -1.86e+01 3.711e-03 -2.59e+01 -2.65e+01
SSE.5 Torque^2 1.177e-01 -1.21e+01 -1.27e+01 1.641e-02 -2.00e+01 -2.06e+01
SSE.7 Utility Gross 1.295e-02 -1.89e+01 -2.02e+01 2.331e-03 -2.58e+01 -2.70e+01
SSE.9 Utility Net 1.294e-02 -1.89e+01 -2.02e+01 2.271e-03 -2.59e+01 -2.71e+01
SSE.10 Utility Gross Combined Alpha 6.200e-04 -3.11e+01 -3.23e+01 7.443e-04 -3.04e+01 -3.16e+01
SSE.11 Utility Net Combined Alpha 6.668e-05 -4.00e+01 -4.12e+01 4.246e-04 -3.26e+01 -3.38e+01

5.7.5.2 Normalized

Table 5.21: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.683e-02 -1.99e+01 -2.05e+01 3.270e-02 -1.72e+01 -1.78e+01
SSE.3 Met Cost Gross 1.914e-03 -2.86e+01 -2.92e+01 1.153e-02 -2.14e+01 -2.20e+01
SSE.4 Met Cost Net 2.137e-03 -2.81e+01 -2.88e+01 1.197e-02 -2.12e+01 -2.19e+01
SSE.5 Torque^2 1.425e+00 -2.13e+00 -2.74e+00 2.234e-01 -9.54e+00 -1.02e+01
SSE.7 Utility Gross 2.128e-04 -3.54e+01 -3.66e+01 6.779e-03 -2.15e+01 -2.27e+01
SSE.9 Utility Net 1.236e-04 -3.75e+01 -3.88e+01 5.337e-03 -2.25e+01 -2.37e+01
SSE.10 Utility Gross Combined Alpha 2.211e-04 -3.52e+01 -3.64e+01 6.845e-03 -2.15e+01 -2.27e+01
SSE.11 Utility Net Combined Alpha 1.517e-04 -3.67e+01 -3.79e+01 6.167e-03 -2.19e+01 -2.31e+01

5.7.6 SSE of models - Exp 2b to 2c

5.7.6.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.22: Exp 2c - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.653e-02 -1.58e+01 -1.64e+01 5.754e-02 -1.50e+01 -1.56e+01
SSE.3 Met Cost Gross 1.972e-03 -2.85e+01 -2.91e+01 2.861e-02 -1.78e+01 -1.84e+01
SSE.4 Met Cost Net 1.649e-01 -1.08e+01 -1.14e+01 8.275e-02 -1.35e+01 -1.41e+01
SSE.5 Torque^2 1.021e-01 -1.27e+01 -1.33e+01 3.730e-02 -1.67e+01 -1.73e+01
SSE.7 Utility Gross 1.262e-01 -9.83e+00 -1.11e+01 7.578e-02 -1.19e+01 -1.31e+01
SSE.9 Utility Net 1.257e-01 -9.84e+00 -1.11e+01 7.554e-02 -1.19e+01 -1.31e+01
SSE.10 Utility Gross Combined Alpha 7.079e-02 -1.21e+01 -1.34e+01 6.403e-02 -1.25e+01 -1.38e+01
SSE.11 Utility Net Combined Alpha 5.715e-02 -1.30e+01 -1.42e+01 6.036e-02 -1.28e+01 -1.40e+01

5.7.6.2 Normalized

Table 5.23: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.905e-02 -1.56e+01 -1.62e+01 3.596e-02 -1.68e+01 -1.75e+01
SSE.3 Met Cost Gross 1.829e-02 -1.95e+01 -2.02e+01 1.351e-02 -2.08e+01 -2.14e+01
SSE.4 Met Cost Net 1.899e-02 -1.94e+01 -2.00e+01 1.399e-02 -2.06e+01 -2.12e+01
SSE.5 Torque^2 1.213e+00 -2.77e+00 -3.39e+00 2.153e-01 -9.69e+00 -1.03e+01
SSE.7 Utility Gross 1.069e-02 -1.97e+01 -2.09e+01 8.325e-03 -2.07e+01 -2.19e+01
SSE.9 Utility Net 8.293e-03 -2.07e+01 -2.19e+01 6.716e-03 -2.16e+01 -2.28e+01
SSE.10 Utility Gross Combined Alpha 1.080e-02 -1.97e+01 -2.09e+01 8.397e-03 -2.07e+01 -2.19e+01
SSE.11 Utility Net Combined Alpha 9.647e-03 -2.01e+01 -2.13e+01 7.642e-03 -2.10e+01 -2.23e+01

5.8 2c Durations

5.8.1 DF Creation

5.8.2 Peak Velocity Plotting

5.8.3 SSE of models - Exp 2c

The utility combined alpha is using the alpha value predicted off fitting a utility model to the preferred and small target experiement at the same time. This alpha value is used to make figure 5.2.

5.8.3.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions.

Table 5.24: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.653e-02 -1.58e+01 -1.64e+01 5.754e-02 -1.50e+01 -1.56e+01
SSE.3 Met Cost Gross 1.972e-03 -2.85e+01 -2.91e+01 2.861e-02 -1.78e+01 -1.84e+01
SSE.4 Met Cost Net 1.649e-01 -1.08e+01 -1.14e+01 8.275e-02 -1.35e+01 -1.41e+01
SSE.5 Torque^2 1.021e-01 -1.27e+01 -1.33e+01 3.730e-02 -1.67e+01 -1.73e+01
SSE.7 Utility Gross 9.692e-04 -2.93e+01 -3.05e+01 2.972e-02 -1.56e+01 -1.68e+01
SSE.9 Utility Net 1.132e-03 -2.87e+01 -2.99e+01 3.115e-02 -1.54e+01 -1.66e+01
SSE.10 Utility Gross Combined Alpha 7.079e-02 -1.21e+01 -1.34e+01 6.403e-02 -1.25e+01 -1.38e+01
SSE.11 Utility Net Combined Alpha 5.715e-02 -1.30e+01 -1.42e+01 6.036e-02 -1.28e+01 -1.40e+01

5.8.3.2 Normalized

Table 5.25: Exp 2a - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.905e-02 -1.56e+01 -1.62e+01 3.596e-02 -1.68e+01 -1.75e+01
SSE.3 Met Cost Gross 1.829e-02 -1.95e+01 -2.02e+01 1.351e-02 -2.08e+01 -2.14e+01
SSE.4 Met Cost Net 1.899e-02 -1.94e+01 -2.00e+01 1.399e-02 -2.06e+01 -2.12e+01
SSE.5 Torque^2 1.213e+00 -2.77e+00 -3.39e+00 2.153e-01 -9.69e+00 -1.03e+01
SSE.7 Utility Gross 9.813e-03 -2.00e+01 -2.13e+01 7.732e-03 -2.10e+01 -2.22e+01
SSE.9 Utility Net 9.535e-03 -2.02e+01 -2.14e+01 7.583e-03 -2.11e+01 -2.23e+01
SSE.10 Utility Gross Combined Alpha 1.080e-02 -1.97e+01 -2.09e+01 8.397e-03 -2.07e+01 -2.19e+01
SSE.11 Utility Net Combined Alpha 9.647e-03 -2.01e+01 -2.13e+01 7.642e-03 -2.10e+01 -2.23e+01

5.8.4 2c Modeling Plot

Modeling Results

Figure 5.5: Modeling Results

5.8.5 SSE of models - Exp 2c to 2a

5.8.5.1 Absolute

This table shows the SSE for the 2b movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.26: Exp 2b - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 3.867e-03 -2.58e+01 -2.64e+01 7.421e-04 -3.24e+01 -3.30e+01
SSE.3 Met Cost Gross 6.272e-02 -1.46e+01 -1.52e+01 3.904e-03 -2.57e+01 -2.63e+01
SSE.4 Met Cost Net 2.695e-02 -1.80e+01 -1.86e+01 3.711e-03 -2.59e+01 -2.65e+01
SSE.5 Torque^2 1.177e-01 -1.21e+01 -1.27e+01 1.641e-02 -2.00e+01 -2.06e+01
SSE.7 Utility Gross 5.614e-02 -1.31e+01 -1.43e+01 3.321e-03 -2.44e+01 -2.56e+01
SSE.9 Utility Net 5.080e-02 -1.35e+01 -1.47e+01 2.867e-03 -2.50e+01 -2.62e+01
SSE.10 Utility Gross Combined Alpha 6.200e-04 -3.11e+01 -3.23e+01 7.443e-04 -3.04e+01 -3.16e+01
SSE.11 Utility Net Combined Alpha 6.668e-05 -4.00e+01 -4.12e+01 4.246e-04 -3.26e+01 -3.38e+01

5.8.5.2 Normalized

Table 5.27: Exp 2b - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 1.683e-02 -1.99e+01 -2.05e+01 3.270e-02 -1.72e+01 -1.78e+01
SSE.3 Met Cost Gross 1.914e-03 -2.86e+01 -2.92e+01 1.153e-02 -2.14e+01 -2.20e+01
SSE.4 Met Cost Net 2.137e-03 -2.81e+01 -2.88e+01 1.197e-02 -2.12e+01 -2.19e+01
SSE.5 Torque^2 1.425e+00 -2.13e+00 -2.74e+00 2.234e-01 -9.54e+00 -1.02e+01
SSE.7 Utility Gross 1.397e-04 -3.71e+01 -3.83e+01 6.245e-03 -2.18e+01 -2.31e+01
SSE.9 Utility Net 1.497e-04 -3.68e+01 -3.80e+01 6.109e-03 -2.19e+01 -2.32e+01
SSE.10 Utility Gross Combined Alpha 2.211e-04 -3.52e+01 -3.64e+01 6.845e-03 -2.15e+01 -2.27e+01
SSE.11 Utility Net Combined Alpha 1.517e-04 -3.67e+01 -3.79e+01 6.167e-03 -2.19e+01 -2.31e+01

5.8.6 SSE of models - Exp 2c to 2b

5.8.6.1 Absolute

This table shows the SSE for the 2c movement duration and peak velocity predictions. These SSE’s are calculated from only taking the predicted durations as before, and seeing how they compare to 2b. No new model fitting was done.

Table 5.28: Exp 2c - Sum squared errors for movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.653e-02 -1.58e+01 -1.64e+01 5.754e-02 -1.50e+01 -1.56e+01
SSE.3 Met Cost Gross 1.972e-03 -2.85e+01 -2.91e+01 2.861e-02 -1.78e+01 -1.84e+01
SSE.4 Met Cost Net 1.649e-01 -1.08e+01 -1.14e+01 8.275e-02 -1.35e+01 -1.41e+01
SSE.5 Torque^2 1.021e-01 -1.27e+01 -1.33e+01 3.730e-02 -1.67e+01 -1.73e+01
SSE.7 Utility Gross 9.692e-04 -2.93e+01 -3.05e+01 2.972e-02 -1.56e+01 -1.68e+01
SSE.9 Utility Net 1.132e-03 -2.87e+01 -2.99e+01 3.115e-02 -1.54e+01 -1.66e+01
SSE.10 Utility Gross Combined Alpha 7.079e-02 -1.21e+01 -1.34e+01 6.403e-02 -1.25e+01 -1.38e+01
SSE.11 Utility Net Combined Alpha 5.715e-02 -1.30e+01 -1.42e+01 6.036e-02 -1.28e+01 -1.40e+01

5.8.6.2 Normalized

Table 5.29: Exp 2c - Sum squared errors for NORMALIZED movement duration and peak velocity.
Model Movement Duration SSE Movement Duration AIC Movement Duration BIC Peak Velocity SSE Peak Velocity AIC Peak Velocity BIC
SSE.2 Accuracy Prob 4.905e-02 -1.56e+01 -1.62e+01 3.596e-02 -1.68e+01 -1.75e+01
SSE.3 Met Cost Gross 1.829e-02 -1.95e+01 -2.02e+01 1.351e-02 -2.08e+01 -2.14e+01
SSE.4 Met Cost Net 1.899e-02 -1.94e+01 -2.00e+01 1.399e-02 -2.06e+01 -2.12e+01
SSE.5 Torque^2 1.213e+00 -2.77e+00 -3.39e+00 2.153e-01 -9.69e+00 -1.03e+01
SSE.7 Utility Gross 9.813e-03 -2.00e+01 -2.13e+01 7.732e-03 -2.10e+01 -2.22e+01
SSE.9 Utility Net 9.535e-03 -2.02e+01 -2.14e+01 7.583e-03 -2.11e+01 -2.23e+01
SSE.10 Utility Gross Combined Alpha 1.080e-02 -1.97e+01 -2.09e+01 8.397e-03 -2.07e+01 -2.19e+01
SSE.11 Utility Net Combined Alpha 9.647e-03 -2.01e+01 -2.13e+01 7.642e-03 -2.10e+01 -2.23e+01